US10505620B2 - Receiving apparatus and receiving method, and program and recording medium - Google Patents

Receiving apparatus and receiving method, and program and recording medium Download PDF

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US10505620B2
US10505620B2 US16/079,508 US201716079508A US10505620B2 US 10505620 B2 US10505620 B2 US 10505620B2 US 201716079508 A US201716079508 A US 201716079508A US 10505620 B2 US10505620 B2 US 10505620B2
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transmission channel
threshold value
delay times
arriving
estimated
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US20190068273A1 (en
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Naosuke Ito
Daisuke Shimbo
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Mitsubishi Electric Corp
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Mitsubishi Electric Corp
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/10—Polarisation diversity; Directional diversity
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/74—Multi-channel systems specially adapted for direction-finding, i.e. having a single antenna system capable of giving simultaneous indications of the directions of different signals
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q21/00—Antenna arrays or systems
    • H01Q21/24—Combinations of antenna units polarised in different directions for transmitting or receiving circularly and elliptically polarised waves or waves linearly polarised in any direction
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/309—Measuring or estimating channel quality parameters
    • H04B17/364—Delay profiles
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/086—Weighted combining using weights depending on external parameters, e.g. direction of arrival [DOA], predetermined weights or beamforming
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/0204—Channel estimation of multiple channels
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/0212—Channel estimation of impulse response
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04J—MULTIPLEX COMMUNICATION
    • H04J11/00—Orthogonal multiplex systems, e.g. using WALSH codes

Definitions

  • the present invention relates to a receiving method and a receiving apparatus, and, in particular, to a technique for receiving radio waves transmitted from a transmitter, and identifying the arrival direction of the direct wave based on the received signal.
  • the present invention also relates to a program for causing a computer to execute the processes in the above-mentioned receiving apparatus or receiving method, and a computer-readable recording medium in which the above-mentioned program is recorded.
  • the reception performance is degraded due to the effects of the arriving waves (hereinafter called “delayed waves”), which arrive after reflection or scattering on buildings, vehicles, or the like, in addition to the arriving wave (hereinafter called “a direct wave”) which arrives directly from the transmitter.
  • delayed waves which arrive after reflection or scattering on buildings, vehicles, or the like
  • a direct wave which arrives directly from the transmitter.
  • An environment in which a plurality of arriving waves are present is called a multipath environment.
  • a known technique to reduce the degradation in the performance due to multipath is a directivity control using an array antenna.
  • An array antenna has a plurality of antenna elements, and can be made to have a directivity by controlling weighting coefficients used for combining signals received by the antenna elements.
  • the degradation in the performance due to the influence of the delayed waves can be mitigated by controlling the directivity so that the main lobe is directed to the direction in which the direct wave arrives.
  • the directivity may be manually adjusted so that the main lobe of the array antenna is directed to the transmitter.
  • the radio waves are received at a moving body such as a vehicle, for instance, in a case of reception in an inter-vehicle communication, manual adjustment is not feasible because the position of the transmitter relative to the receiving apparatus changes with the movement of the vehicle. It is therefore necessary to automatically estimate the arrival direction of the direct wave, from the received signal in which the direct wave and the delayed waves are multiplexed.
  • Radio wave environments for the wireless communications can be classified into LOS (Line Of Sight) in which the transmitter is in a visual line of sight from the receiver, and NLOS (None Line Of Sight) in which there is no visual line of sight between the transmitter and the receiver.
  • LOS Line Of Sight
  • NLOS Near Line Of Sight
  • the present invention assumes the LOS environment.
  • Patent Reference 1 describes an apparatus in which the multipath arrival directions are measured based on signals received by two antennas.
  • the frequency characteristic (transfer function in the frequency domain) of the transmission channel is estimated from the signal received by each antenna element, the estimated transmission channel frequency characteristic is inverse-Fourier transformed to determine a complex delay profile, the arriving waves of different delay times are separated from the complex delay profile, and the arrival angle is estimated on the basis of the phase difference between the separated direct waves received by the antenna elements.
  • Patent Reference 2 discloses estimation of the delay times by a super-resolution process, such as an MUSIC (MUltiple SIgnal Classification) process, or an ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) process.
  • MUSIC MUltiple SIgnal Classification
  • ESPRIT Estimat of Signal Parameters via Rotational Invariance Techniques
  • the signals received by a plurality of antennas are transformed into a frequency spectrum
  • the delay time of each arriving wave is estimated by a super-resolution process using the frequency spectrum
  • the estimation results are used to estimate a coefficient matrix in which the arriving waves are included
  • the above-mentioned frequency spectrum is multiplied by a pseudo-inverse matrix of the above-mentioned coefficient matrix to separate the components of the direct waves
  • the arrival angle is estimated from the phase differences among the separated direct waves.
  • Patent Reference 1 The technique shown in Patent Reference 1 is associated with a problem in that the direct wave and the delayed waves cannot be separated when the delay times are short. For example, when a building, a vehicle or the like is present in the neighborhood of the receiver, there is no significant difference in the length of the radio wave propagation path from the transmitter to the receiver between the direct wave and the delayed waves, so that delay times are very short. If the delay times are shorter than the delay time resolution of the complex delay profile, the direct wave and the delayed waves overlap each other in the estimated complex delay profile, and cannot be separated from each other. As a result, the arrival angle estimation accuracy is lowered substantially.
  • the delay time, 20 ns is shorter than the delay time resolution, 100 ns, and the direct wave and the delayed wave overlap each other in the estimated delay profile, with the result that the accuracy of estimation of the arrival angle is lowered.
  • Patent Reference 2 The method disclosed in Patent Reference 2 is associated with a problem that the amount of the processes necessary to separate the arriving wave, in particular the amount of the calculation of the pseudo-inverse matrix is large.
  • An object of the present invention is to provide a receiving apparatus and method which can accurately estimate the arrival angle of the direct wave in an environment in which delayed waves of short delay times are present, and with which the amount of required calculation can be reduced.
  • a receiving apparatus for receiving radio waves transmitted from a transmitter, and estimating an arrival angle of a direct wave from the transmitter, comprising:
  • first to N-th (N being an integer not less than 2) wireless reception units provided respectively corresponding to first to N-th antenna elements forming an array antenna, and performing frequency conversion and AD conversion on first to N-th analog signals obtained by receiving the radio waves by said first to N-th antenna elements, respectively, to output first to N-th digital signals;
  • first to N-th transmission channel estimation units for estimating transmission channel frequency characteristics based on the first to N-th digital signals, respectively, and outputting first to N-th transmission channel estimation results
  • a delay time estimation unit for estimating, by means of a super-resolution process, delay times of one or more arriving waves included in the radio waves, based on a transmission channel estimation result among the first to N-th transmission channel estimation results;
  • a delay time grouping unit for comparing the delay times estimated by said delay time estimation unit with a threshold value, to determine whether the estimated delay times are shorter than the threshold value
  • first to N-th delayed wave removal units provided respectively corresponding to said first to N-th transmission channel estimation units, removing, from the first to N-th transmission channel estimation results, an arriving wave component corresponding to the delay time which said delay time grouping unit has determined to be equal to or more than the threshold value, and outputting first to N-th transmission channel frequency characteristics pertaining to the arriving waves of the delay times which said delay time grouping unit has determined to be shorter than the threshold value;
  • first to N-th arriving wave separation units provided respectively corresponding to said first to N-th delayed wave removal units, and respectively separating, from each other, arriving wave components included in the first to N-th transmission channel frequency characteristics to extract first to N-th direct wave components;
  • an arrival angle estimation unit for estimating an arrival angle of the direct wave based on a phase difference among the first to N-th direct wave components.
  • the direct wave and the delayed wave are separated after estimating the delay times by a super-resolution process, so that the arrival angle of the direct wave can be accurately estimated even in an environment in which a delayed wave of a short delay time is present. Also, the calculation of the pseudo-inverse matrix, etc. is performed after removing a relatively long delay time, so that the amount of calculation can be reduced.
  • FIG. 1 is a block diagram showing a receiving apparatus of a first embodiment of the present invention.
  • FIG. 2 is a block diagram showing an example of a configuration of the transmission channel estimation unit in FIG. 1 .
  • FIG. 3 is a block diagram showing another example of a configuration of the transmission channel estimation unit in FIG. 1 .
  • FIG. 4 is a block diagram showing an example of a configuration of the delayed wave removal unit in FIG. 1 .
  • FIG. 5( a ) is a diagram showing an example of a delay profile before the removal of the delayed waves by the delayed wave removal unit in FIG. 1
  • FIG. 5( b ) and FIG. 5( c ) are diagrams showing different examples of the delay profiles after the removal.
  • FIG. 6 is a diagram schematically illustrating the arrival angle of the direct wave.
  • FIG. 7 is a block diagram showing an example of a configuration of the arrival angle estimation unit in FIG. 1 .
  • FIG. 8 is a block diagram showing a receiving apparatus of a second embodiment of the present invention.
  • FIG. 9 is a block diagram showing a receiving apparatus of a third embodiment of the present invention.
  • FIG. 10 is a flowchart showing the procedure of the processes in a receiving method of a fourth embodiment of the present invention.
  • FIG. 11 is a flowchart showing the procedure of the processes in an example of the transmission channel estimation step in FIG. 10 .
  • FIG. 12 is a flowchart showing the procedure of the processes in another example of the transmission channel estimation step in FIG. 10 .
  • FIG. 13 is a flowchart showing the procedure of the processes in an example of the delayed wave removal step in FIG. 10 .
  • FIG. 14 is a flowchart showing the procedure of the processes in an example of the arrival angle estimation step in FIG. 10 .
  • FIG. 15 is a flowchart showing the procedure of the processes in a receiving method of a fifth embodiment of the present invention.
  • FIG. 16 is a flowchart showing the procedure of the processes in a receiving method of the sixth embodiment of the present invention.
  • FIG. 17 is a block diagram showing a computer executing the processes in the first to sixth embodiments.
  • FIG. 1 shows a receiving apparatus of the present embodiment.
  • the illustrated receiving apparatus is for receiving radio waves transmitted from a transmitter, and estimating the direction of the transmitter, i.e., the arrival direction of the direct wave.
  • the illustrated receiving apparatus comprises wireless reception units 11 - 1 , 11 - 2 , transmission channel estimation units 12 - 1 , 12 - 2 , a delay time estimation unit 13 , a delay time grouping unit 14 , delayed wave removal units 15 - 1 , 15 - 2 , a pseudo-inverse matrix generation unit 16 , arriving wave separation units 17 - 1 , 17 - 2 , and an arrival angle estimation unit 18 .
  • the wireless reception units 11 - 1 , 11 - 2 are respectively connected to antenna elements 10 - 1 , 10 - 2 .
  • the wireless reception unit 11 - 1 , the transmission channel estimation unit 12 - 1 , the delayed wave removal unit 15 - 1 , and the arriving wave separation unit 17 - 1 form a first system, and are provided corresponding to each other, and also corresponding to the first antenna element 10 - 1 .
  • the wireless reception unit 11 - 2 , the transmission channel estimation unit 12 - 2 , the delayed wave removal unit 15 - 2 , and the arriving wave separation unit 17 - 2 form a second system, and are provided corresponding to each other, and also corresponding to the second antenna element 10 - 2 .
  • the processes in the first system and the processes in the second system are similar. However, the signals input to the respective systems differ (that is they are the signals obtained by the antenna elements 10 - 1 , 10 - 2 , respectively).
  • the delay time estimation unit 13 the delay time grouping unit 14 , the pseudo-inverse matrix generation unit 16 , and the arrival angle estimation unit 18 are provided in common for the above-mentioned two systems.
  • the receiving apparatus shown in FIG. 1 has a Configuration for the case where the number of the antenna elements is two.
  • the present invention is applicable even when the number of the antenna elements is three or more, so that, in the following description, the number of antenna elements may sometimes be represented by N.
  • the wireless reception units 11 - 1 , 11 - 2 in FIG. 1 are provided respectively corresponding to the antenna elements 10 - 1 , 10 - 2 , and each frequency-convert the analog signal obtained by reception of the radio waves at the corresponding antenna element, into a baseband signal, AD-convert the baseband signal to generate a digital signal Sr n (n being 1 or 2), and output the generated digital signal Sr n .
  • the transmission channel estimation units 12 - 1 , 12 - 2 in FIG. 1 are provided respectively corresponding to the wireless reception units 11 - 1 , 11 - 2 , and each estimate the frequency characteristic (transfer function in the frequency domain) of the transmission channel, on the basis of the digital signal Sr n output from the corresponding wireless reception unit.
  • the method of estimating the transmission channel frequency characteristic depends on the transmission scheme adopted by the communication system.
  • the present invention is applicable to any transmission scheme.
  • the following description relates to a case in which the OFDM (Orthogonal Frequency Division Multiplex) transmission scheme is adopted, and a case in which the DSSS (Direct Sequence Spectrum Spread) transmission scheme is adopted.
  • the OFDM transmission scheme and the DSSS transmission scheme are adopted in many communication systems.
  • the OFDM transmission scheme In the OFDM transmission scheme, symbols are generated by multiplexing a plurality of subcarriers which are orthogonal with each other, and transmission is performed symbol by symbol.
  • part of the subcarriers are used as pilot subcarriers which are known at the transmission side and the reception side, in order to compensate for the transmission channel distortion at the reception side.
  • the pilot subcarriers are used to estimate the transmission channel frequency characteristic.
  • FIG. 2 shows an example of a transmission channel estimation unit 12 - n (n being 1 or 2) used when the OFDM transmission scheme is adopted.
  • the transmission channel estimation unit 12 - n shown in FIG. 2 comprises an FFT unit 20 - n , a pilot extraction unit 21 - n , a pilot generation unit 22 - n , a division unit 23 - n , and an interpolation unit 24 - n.
  • the FFT unit 20 - n converts the digital signal Sr n output from the wireless reception unit 11 - n shown in FIG. 1 , symbol by symbol, from the time axis into the frequency axis, by FFT (Fast-Fourier Transform), thereby to output subcarriers.
  • the pilot extraction unit 21 - n extracts pilot carriers from the subcarriers output from the FFT unit 20 - n.
  • the pilot generation unit 22 - n generates pilot carriers known in the receiving apparatus.
  • the division unit 23 - n divides the pilot carriers extracted by the pilot extraction unit 21 - n , by the pilot carriers generated by the pilot generation unit 22 - n , thereby to output the frequency characteristic of the transmission channel acting on the pilot carriers.
  • the interpolation unit 24 - n performs interpolation based on the frequency characteristics of the transmission channel acting on the pilot carriers in the symbol direction and the subcarrier direction, to obtain frequency characteristics of the transmission channel (transmission channel estimation results) for all the subcarriers.
  • the DSSS transmission scheme signals spread by using a pseudonoise sequence, symbol by symbol, are transmitted, and despread at the reception side.
  • FIG. 3 shows an example of a transmission channel estimation unit 12 - n (n being 1 or 2) used when the DSSS transmission scheme is adopted.
  • the transmission channel estimation unit 12 - n shown in FIG. 3 has a pseudonoise sequence generation unit 25 - n , a despreading unit 26 - n , and an FFT unit 27 - n.
  • the pseudonoise sequence generation unit 25 - n generates a pseudonoise sequence Ns which is identical to the pseudonoise sequence used at the time of spreading at the transmission side.
  • the despreading unit 26 - n calculates a sliding correlation between the digital signal Sr n output from the wireless reception unit 11 - n in FIG. 1 , and the pseudonoise sequence Ns, symbol by symbol, and outputs the calculated sliding correlation.
  • the FFT unit 27 - n transforms, by FFT, the output of the despreading unit 26 - n into the frequency domain, to obtain the transmission channel frequency characteristic (transmission channel estimation result).
  • the transmission channel frequency characteristic (transmission channel estimation result) output by the transmission channel estimation unit 12 - n can be represented as a column vector consisting of components of respective frequencies f 1 to f M , by the following equation (1).
  • f m (m being any of 1 to M) denotes a frequency at a point when the range of the lowest frequency f 1 to the highest frequency f M is equally divided into M sections, with the division number M being the number of FFT points at the FFT unit 20 - n in FIG. 2 or the FFT unit 27 - n in FIG. 3 .
  • the delay time estimation unit 13 estimates the delay times of one or more arriving waves included in the radio waves received by the corresponding antenna element 10 - 1 .
  • the delay time estimation is performed by a super-resolution process, such as the MUSIC (MUltiple SIgnal Classification) process, the ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) process.
  • MUSIC MUltiple SIgnal Classification
  • ESPRIT Estimat of Signal Parameters via Rotational Invariance Techniques
  • the number of the arriving waves is denoted by K
  • the delay times of the respective arriving waves are denoted by ⁇ 1 , ⁇ 2 , . . . ⁇ K
  • the estimated values of the delay times are denoted by ⁇ (hat) 1 , ⁇ (hat) 2 , . . . , ⁇ (hat) K .
  • ⁇ 1 ⁇ 2 ⁇ . . . ⁇ K it is assumed that ⁇ 1 ⁇ 2 ⁇ . . . ⁇ K .
  • the delay time grouping unit 14 compares the delay time estimation results ⁇ (hat) 1 , . . . , ⁇ (hat) K output by the delay time estimation unit 13 , with a predetermined threshold value ⁇ th , and determines whether each estimated value ⁇ (hat) k is shorter than the threshold value ⁇ th .
  • the delay time grouping unit 14 then groups the estimated values ⁇ (hat) 1 , . . . , ⁇ (hat) K , into those ⁇ (hat) 1 , . . . , ⁇ (hat) q , which are shorter than the threshold value ⁇ th , and other estimated values ⁇ (hat) q+1 , . . .
  • ⁇ (hat) K (those which are equal to or longer than the threshold value ⁇ th ).
  • the threshold value ⁇ th is so determined that the relation ⁇ (hat) 1 ⁇ th ⁇ (hat) K is satisfied.
  • the delay time grouping unit 14 outputs the estimated values ⁇ (hat) 1 , . . . , ⁇ (hat) q having been determined to be shorter than the threshold value ⁇ th , and do not output the estimated values ⁇ (hat) q+1 , . . . , ⁇ (hat) K having been determined to be equal or longer than the threshold value ⁇ th .
  • the delay time grouping unit 14 may alternatively output information indicating whether each estimated value ⁇ (hat) k is shorter than the threshold value ⁇ th .
  • the delayed wave removal units 15 - 1 , 15 - 2 are provided respectively corresponding to the transmission channel estimation units 12 - 1 , 12 - 2 , and each remove the arriving wave components corresponding to the delay times which the delay time grouping unit 14 has determined to be equal to or longer than the threshold value ⁇ th , from the output of the corresponding transmission channel estimation unit (transmission channel estimation result). That is, each delayed wave removal unit 15 - n removes, from the transmission channel frequency characteristic estimation result output from the corresponding transmission channel estimation unit 12 - n , the delayed wave components corresponding to the delay times ⁇ (hat) q+1 , . . . , ⁇ (hat) K which the delay time grouping unit 14 has determined to be equal to or longer than the threshold value ⁇ th .
  • the delayed wave removal unit 15 - n comprises an IFFT unit 50 - n , a delayed wave component removal unit 51 - n , and an FFT unit 52 - n , as shown in FIG. 4 .
  • the IFFT unit 50 - n performs IFFT (Inverse Fast-Fourier Transform), on the estimation result z n of the transmission channel frequency characteristic shown in the equation (1), to determine a delay profile.
  • IFFT Inverse Fast-Fourier Transform
  • the delayed wave component removal unit 51 - n substitutes 0's for the components corresponding to the delay time estimated values ⁇ (hat) q+1 , . . . , ⁇ (hat) K in the delay profile ( FIG. 5( a ) ) determined by the IFFT unit 50 - n .
  • a delay profile (post-removal delay profile) which does not include the components corresponding to ⁇ (hat) q+1 , . . . , ⁇ (hat) K , and includes the components corresponding to ⁇ (hat) 1 , . . . , ⁇ (hat) q , as shown in FIG. 5( b ) , is generated.
  • the FFT unit 52 - n performs FFT on the output ( FIG. 5( b ) ) of the delayed wave component removal unit 51 - n , to restore a signal in the frequency domain.
  • a transmission channel frequency characteristic which does not include the arriving wave components corresponding to ⁇ (hat) q+1 , . . . , ⁇ (hat) K , and which includes the arriving wave components corresponding to ⁇ (hat) 1 , . . . , ⁇ (hat) q is obtained.
  • the delayed wave component removal unit 51 - n may substitute 0's for all the components in the range of ⁇ (hat) q+1 , . . . , ⁇ (hat) K in the delay profile.
  • a result of this process is shown in FIG. 5( c ) .
  • FIG. 5( c ) not only the components corresponding to ⁇ (hat) q+1 , . . . , ⁇ (hat) K , in the delay profile in FIG. 5( a ) , but also the noise components in the range of these components have been replaced with 0's.
  • the input signal and the output signal of the delayed wave removal unit 15 - n can be represented by matrixes.
  • the input signal which is represented by the above equation (1), can also be represented by the following equation (2).
  • [Mathematical Expression 2] z n X ⁇ y n (2)
  • X denotes a matrix representing the delay times, and can be represented by the following equation (3).
  • K denotes the number of the arriving waves as mentioned above
  • M denotes the frequency division number as mentioned above.
  • the distance between the antenna element 10 - 1 and the antenna element 10 - 2 is in the order of half the wavelength, so that it is assumed that there is no difference in the delay time between the antenna elements.
  • Equation (2) denotes a column vector consisting of components representing the amplitude and the phase of each of all the arriving waves (first to K-th arriving waves), and can be represented by the following equation (4).
  • the output signal of the delayed wave removal unit 15 - n is explained. If the estimated values of the delay times which the delay time grouping unit 14 has determined to be equal to or longer than the threshold value ⁇ th to are equal to the actual delay times, such delayed wave components are removed by the delayed wave removal unit 15 - n .
  • X′ denotes what is obtained by removing the components corresponding to the delay times ⁇ q+1 , . . . , ⁇ K from X, and is represented by the equation (6).
  • y′ n denotes what is obtained by removing the components corresponding to the delay times ⁇ q+1 , see, from y n , and is represented by the equation (7).
  • the output of the delayed wave removal unit 15 - n is a transmission channel frequency characteristic pertaining to the arriving waves of the delay times ⁇ (hat) 1 , . . . , ⁇ (hat) q , which the delay time grouping unit 14 has determined to be shorter than the threshold value ⁇ th , and the size of the matrix X representing the delay times is reduced from M ⁇ K to M ⁇ q.
  • the pseudo-inverse matrix generation unit 16 calculates a matrix represented by the following equation (8), from the delay times ⁇ (hat) 1 , . . . , ⁇ (hat) q which the delay time grouping unit 14 has determined to be shorter than the threshold value ⁇ th .
  • X(hat) + represented by the equation (8) is called a pseudo-inverse matrix of X(hat)′.
  • ⁇ circumflex over (X) ⁇ + ( ⁇ circumflex over (X) ⁇ ′ H ⁇ circumflex over (X) ⁇ ′) ⁇ 1 ⁇ circumflex over (X) ⁇ ′ H (8)
  • X(hat)′ denotes a matrix of the estimated values of the delay times which the delay time grouping unit 14 has determined to be shorter than the threshold value ⁇ th , and is represented by the following equation (9).
  • the matrix represented by the equation (9) is generated based on the delay times ⁇ (hat) 1 , . . . , ⁇ (hat) q which the delay time grouping unit 14 has determined to be shorter than the threshold value ⁇ th , and the process of determining the pseudo-inverse matrix in the equation (8) is performed using the matrix of the equation (9).
  • the size of the matrix X(hat)′ H X(hat)′ on which the inverse matrix computation is performed is q ⁇ q.
  • the size of the matrix on which the inverse matrix computation is performed is K ⁇ K.
  • the arriving wave separation units 17 - 1 , 17 - 2 are provided respectively corresponding to the delayed wave removal units 15 - 1 , 15 - 2 , and each separate, from each other, arriving wave components included in the output of the corresponding delayed wave removal unit, to extract the direct wave component.
  • each arriving wave separation unit 17 - n multiplies the output z′ n (equation (5)) of the corresponding delayed wave removal unit 15 - n , by the pseudo-inverse matrix X(hat) + (equation (8)) generated by the pseudo-inverse matrix generation unit 16 , and extracts the direct wave component from the multiplication result.
  • the above multiplication is represented by the following equation (10).
  • [Mathematical Expression 10] ⁇ ′ n ⁇ circumflex over (X) ⁇ + ⁇ z′ n (10)
  • y(hat)′ n in the equation (10) is the result of estimation of y′ n in the equation (7), and denotes a column vector represented by the following equation (11).
  • the arriving wave separation unit 17 - n also extracts the value a(hat) n,1 at the top of the above-mentioned column vector y(hat)′ n , and outputs it as the direct wave component.
  • the arrival angle estimation unit 18 calculates the phase difference between the direct wave component a(hat)) 1,1 extracted by the arriving wave separation unit 17 - 1 , and the direct wave component a(hat) 2,1 extracted by the arriving wave separation unit 17 - 2 , and estimates the arrival direction of the direct wave based on the calculated phase difference.
  • the arrival direction of the direct wave is determined to be the direction of the transmitter.
  • d p ⁇ sin ⁇ between the propagation path difference d p between the antenna elements, and the arrival angle ⁇
  • d p ⁇ /2 ⁇ between the propagation path difference d p , the wave length ⁇ , and the phase difference ⁇ of the received radio waves.
  • the arrival angle estimation unit 18 comprises a phase difference calculation unit 80 , and an arrival angle calculation unit 81 , as shown in FIG. 7 .
  • the phase difference calculation unit 80 calculates the phase difference ⁇ between the direct wave component a(hat) 1,1 and the direct wave component a(hat) 2,1 .
  • the arrival angle calculation unit 81 determines the arrival angle ⁇ from the phase difference ⁇ , using the relation of the above equation (13).
  • the number of the antenna elements is two. But the invention is applicable to a case where the number of the antenna elements is more than two. In such a case, the phase difference between the antenna elements is determined for each of a plurality of combination patterns, and an average value of the arrival angles for the respective combinations may be calculated.
  • the direct wave and the delayed waves cannot be separated when there are delayed waves of short delay times, and the accuracy of estimation of the arrival angle of the direct wave is lowered.
  • the direct wave and the delayed waves are separated after estimating the delay times of the arriving waves by a super-resolution process, with the result that the arrival angle of the direct wave can be estimated with a high accuracy even if there are delayed waves of short delay times.
  • the arriving waves are separated after removing the delayed wave components of long delay times, from the transmission channel estimation result, so that the amount of calculation required to determine the inverse matrix, which is necessary at the time of the arriving wave separation can be reduced.
  • the number of multiplications required is K 3
  • the number of multiplications is q 3 . Because q ⁇ K, it will be understood that the amount of calculation required for the inverse matrix computation is reduced.
  • the delayed wave removal unit 15 - n performs the processes of FFT and IFFT of M points for the removal of the delayed waves
  • the number of multiplications required for the FFT or IFFT is M ⁇ log (M), and does not depend on the number of the arriving waves, so that the amount of calculation is constant.
  • M log
  • FIG. 8 shows a receiving apparatus of the second embodiment of the present invention.
  • the receiving apparatus shown in FIG. 8 is generally identical to the receiving apparatus in FIG. 1 , but a threshold value determination unit 31 is added.
  • the threshold value determination unit 31 determines the threshold value ⁇ th based on the delay times estimated by the delay time estimation unit 13 .
  • the delay time grouping unit 14 in FIG. 8 is generally identical to the delay time grouping unit 14 in FIG. 1 , but differs in the following respects. That is, the delay time grouping unit 14 in FIG. 1 uses the predetermined threshold value ⁇ th , whereas the delay time grouping unit 14 in FIG. 8 uses the threshold value ⁇ th determined by the threshold value determination unit 31 .
  • the threshold value determination unit 31 uses an intermediate value between the minimum value and the maximum value of the delay times estimated by the delay time estimation unit 13 as the threshold value ⁇ th .
  • a sum of the minimum value of the delay times estimated by the delay time estimation unit 13 and a predetermined value may be used as the threshold value ⁇ th .
  • a sum of a product of the difference between the maximum value and the minimum value of the delay times estimated by the delay time estimation unit 13 , and a predetermined value larger than 0 and smaller than 1, and the above-mentioned minimum value may be used as the threshold value ⁇ th .
  • the threshold value ⁇ th may be any value provided that it is longer than the minimum value and shorter than the maximum value of the delay times estimated by the delay time estimation unit 13 , and, with regard to the manner of its calculation, the present embodiment is not limited to those explained above.
  • the delay times can be grouped into those which are shorter than the threshold value ⁇ th and those which are equal to or longer than the threshold value ⁇ th , and, therefore, part only of the arriving waves estimated in the transmission channel estimation units 12 - 1 , 12 - 2 can be removed.
  • FIG. 9 shows a receiving apparatus of the third embodiment of the present invention.
  • the receiving apparatus shown in FIG. 9 is generally identical to the receiving apparatus in FIG. 1 , but a delay time number discrimination unit 32 is added.
  • the delay time number discrimination unit 32 determines whether the number K of the delay times (corresponding to the number of the arriving waves), estimated by the delay time estimation unit 13 is smaller than a predetermined threshold value K th , and outputs the result ER of the determination.
  • the delay time grouping unit 14 , and the delayed wave removal units 15 - 1 , 15 - 2 in FIG. 9 are generally identical to the delay time grouping unit 14 , and the delayed wave removal units 15 - 1 , 15 - 2 in FIG. 1 , respectively, but differ in the following respects.
  • the delay time grouping unit 14 in FIG. 9 determines whether to carry out the process of the delay time grouping based on the result ER of the determination by the delay time number discrimination unit 32 .
  • the delayed wave removal units 15 - 1 , 15 - 2 in FIG. 9 determine whether to carry out the process of the delayed wave removal based on the result of the determination by the delay time number discrimination unit 32 .
  • the delay time grouping unit 14 does not carry out the process of the delay time grouping, and outputs all the delay times ⁇ 1 to ⁇ K estimated by the delay time estimation unit 13 .
  • the delayed wave removal units 15 - 1 , 15 - 2 do not carry out the processes of the delayed wave removal, and pass on the output z n of the transmission channel estimation units 12 - 1 , 12 - 2 without alteration.
  • Such a column vector y(hat)′ n comprises the components corresponding to all the delay times ⁇ 1 to ⁇ K .
  • the delay time grouping unit 14 carries out the delay time grouping in the same manner as in the first embodiment, and the delayed wave removal units 15 - 1 , 15 - 2 carry out the delayed wave removal in the same manner as in the first embodiment.
  • the number of the delay times corresponds to the number of arriving waves.
  • the number of the arriving waves is small, and the effect of reducing the amount of calculation for the delay time grouping and the delayed wave removal is limited, the amount of processes can be reduced by not carrying out the delay time grouping and the delayed wave removal.
  • the third embodiment has been described as a modification to the first embodiment. Similar modification can be applied to the second embodiment.
  • the fourth embodiment is a receiving method corresponding to the first embodiment.
  • FIG. 10 shows a process procedure in the present embodiment.
  • the receiving method shown in FIG. 10 comprises a wireless reception step ST 11 , a transmission channel estimation step ST 12 , a delay time estimation step ST 13 , a delay time grouping step ST 14 , a delayed wave removal step ST 15 , a pseudo-inverse matrix generation step ST 16 , an arriving wave separation step ST 17 , and an arrival angle estimation step ST 18 .
  • the processes in the wireless reception step ST 11 are similar to the processes performed by the wireless reception units 11 - 1 and 11 - 2 in FIG. 1 .
  • the processes in the transmission channel estimation step ST 12 are similar to the processes performed by the transmission channel estimation units 12 - 1 and 12 - 2 in FIG. 1 .
  • the processes in the delay time estimation step ST 13 are similar to the processes performed by the delay time estimation unit 13 in FIG. 1 .
  • the processes in the delay time grouping step ST 14 are similar to the processes performed by the delay time grouping unit 14 in FIG. 1 .
  • the processes in the delayed wave removal step ST 15 are similar to the processes performed by the delayed wave removal units 15 - 1 and 15 - 2 in FIG. 1 .
  • the processes in the pseudo-inverse matrix generation step ST 16 are similar to the processes performed by the pseudo-inverse matrix generation unit 16 in FIG. 1 .
  • the processes in the arriving wave separation step ST 17 are similar to the processes performed by the arriving wave separation units 17 - 1 and 17 - 2 in FIG. 1 .
  • the processes in the arrival angle estimation step ST 18 are similar to the processes performed by the arrival angle estimation unit 18 in FIG. 1 .
  • first and second analog signals obtained by receiving radio waves by two antenna elements 10 - 1 , 10 - 2 are respectively frequency-converted into baseband signals, and then AD converted to generate first and second digital signals Sr 1 , Sr 2 .
  • transmission channel estimation step ST 12 transmission channel frequency characteristics are estimated, respectively from the first and second digital signals Sr 1 , Sr 2 generated in the wireless reception step ST 11 , and first and second transmission channel estimation results z 1 , z 2 are output.
  • the method of estimating the transmission channel frequency characteristics depends on the transmission scheme adopted in the communication system.
  • the present invention is applicable to any transmission scheme.
  • the following description relates to a case in which the OFDM (Orthogonal Frequency Division Multiplex) transmission scheme, and a case in which the DSSS (Direct Sequence Spectrum Spread) transmission scheme is adopted.
  • the OFDM transmission scheme and the DSSS transmission scheme are adopted in many communication systems.
  • the OFDM transmission scheme In the OFDM transmission scheme, symbols are generated by multiplexing a plurality of subcarriers which are orthogonal to each other, and transmission is performed symbol by symbol.
  • part of the subcarriers are used as pilot subcarriers which are known at the transmission side and the reception side, in order to compensate for the transmission channel distortion at the reception side.
  • the pilot subcarriers are used to estimate the transmission channel frequency characteristics.
  • FIG. 11 shows a procedure of processes in an example of the transmission channel estimation step ST 12 performed in a case in which the OFDM transmission scheme is adopted.
  • the transmission channel estimation step ST 12 shown in FIG. 11 comprises an FFT step ST 20 , a pilot extraction step ST 21 , a pilot generation step ST 22 , a division step ST 23 , and an interpolation step ST 24 .
  • the digital signals Sr 1 , Sr 2 generated in the wireless reception step ST 11 in FIG. 10 are converted from the time axis into the frequency axis by FFT (Fast-Fourier Transform), symbol by symbol, to output respective subcarriers.
  • FFT Fast-Fourier Transform
  • the pilot carriers are extracted from the subcarriers output in the FFT step ST 20 .
  • the processes in the step ST 22 are performed in parallel with the processes in the steps ST 20 and ST 21 .
  • pilot carriers known at the reception side are generated.
  • step ST 21 and the step ST 22 After the step ST 21 and the step ST 22 , the processes in the step ST 23 are performed.
  • the pilot carriers extracted in the pilot extraction step ST 21 are divided by the pilot carriers generated in the pilot generation step ST 22 , to output the frequency characteristics acting on the transmission channel for the pilot carriers.
  • interpolation is performed using the frequency characteristics of the transmission channel acting on the pilot carriers in the symbol direction and in the subcarrier direction, to obtain the frequency characteristics of the transmission channel (transmission channel estimation results) for all the subcarriers.
  • the DSSS transmission scheme signals spread by using a pseudonoise sequence symbol by symbol are transmitted, and despread at the reception side.
  • FIG. 12 shows a procedure of processes in an example of the transmission channel estimation step ST 12 performed when the DSSS transmission scheme is adopted.
  • the transmission channel estimation step ST 12 shown in FIG. 12 comprises a pseudonoise sequence generation step ST 25 , a despreading step ST 26 , and an FFT step ST 27 .
  • pseudonoise sequence generation step ST 25 a pseudonoise sequence Ns which is identical to the pseudonoise sequence used at the time of spreading at the transmission side is generated.
  • the despreading step ST 26 sliding correlations between the digital signals Sr 1 , Sr 2 generated in the wireless reception step ST 11 in FIG. 10 and the pseudonoise sequence Ns are calculated, symbol by symbol.
  • the results of the calculation in the despreading step ST 26 are transformed into the frequency domain by FFT, to obtain the transmission channel frequency characteristics (transmission channel estimation results).
  • the delay time estimation step ST 13 based on either of the first and second transmission channel estimation results z 1 , z 2 , for example, the first transmission channel estimation result z 1 , the delay times of one or more arriving waves included in the radio waves received by the corresponding antenna are estimated.
  • the delay time estimation is performed by a super-resolution process, such as the MUSIC process, or the ESPRIT process.
  • the number of the arriving waves is denoted by K
  • the delay times of the respective arriving waves are denoted by ⁇ 1 , ⁇ 2 , . . . , ⁇ K
  • the estimated values of the delay times are denoted by ⁇ (hat) 1 , ⁇ (hat) 2 , . . . , ⁇ (hat) K .
  • ⁇ 1 ⁇ 2 ⁇ . . . ⁇ K it is assumed that ⁇ 1 ⁇ 2 ⁇ . . . ⁇ K .
  • the delay time estimation results ⁇ (hat) 1 , ⁇ (hat) 2 , . . . , ⁇ (hat) K are compared with a predetermined threshold value ⁇ th , and determination is made as to whether each estimated value ⁇ (hat) k is shorter than the threshold value ⁇ th . Then, the estimated values ⁇ (hat) 1 , . . . , ⁇ (hat) K are grouped into those ⁇ (hat) 1 , . . . , ⁇ (hat) q shorter than the threshold value ⁇ th , and other estimated values ⁇ (hat) q+1 , . . .
  • ⁇ (hat) K (those equal to or longer than the threshold value ⁇ th ).
  • the threshold value ⁇ th is so determined as to satisfy the relation: ⁇ (hat) 1 ⁇ h ⁇ (hat) K .
  • the delayed wave removal step ST 15 from each of the results of the estimation of the transmission channel frequency characteristic in the transmission channel estimation step ST 12 , the delayed wave components corresponding to the delay times ⁇ (hat) q+1 , . . . , ⁇ (hat) K which have been determined to be equal to or longer than the threshold value ⁇ th in the delay time grouping step ST 14 are removed, and the first and second transmission channel frequency characteristics z′ 1 , z′ 2 consisting of the arriving wave components which have not been removed are output.
  • FIG. 13 shows a process procedure in an example of the delayed wave removal step ST 15 .
  • the delayed wave removal step ST 15 shown in FIG. 13 comprises an IFFT step ST 50 , a delayed wave component removal step ST 51 , and an FFT step ST 52 .
  • IFFT is performed on the estimation result z n of the transmission channel frequency characteristic shown in the equation (1), to obtain the delay profile, shown for example in FIG. 5( a ) .
  • the components corresponding to the delay time estimated values ⁇ (hat) q+1 , . . . , ⁇ (hat) K in the delay profile obtained in the IFFT step ST 50 are replaced with 0's, as shown in FIG. 5( b ) .
  • a delay profile (post-removal delay profile) which does not include the components corresponding to ⁇ (hat) q+1 , . . . , ⁇ (hat) K , and includes the components corresponding to ⁇ (hat) 1 , . . . , ⁇ (hat) q is generated.
  • FFT is performed on the output of the delayed wave component removal step ST 51 , so as to restore a signal in the frequency domain.
  • a transmission channel frequency characteristic which does not include the arriving wave components corresponding to ⁇ (hat) q+1 , . . . , ⁇ (hat) K , and includes the arriving wave components corresponding to ⁇ (hat) 1 , . . . , ⁇ (hat) q is obtained.
  • all the components in the range of ⁇ (hat) q+1 , . . . , ⁇ (hat) K in the delay profile in FIG. 5( a ) may be replaced with 0's, as shown in FIG. 5( c ) .
  • the signals generated as a result of the processes of the delayed wave removal step ST 15 represent the transmission channel frequency characteristic pertaining to the delay times ⁇ (hat) 1 , . . . , ⁇ (hat) q which have been determined to be shorter than the threshold value ⁇ th in the delay time grouping step ST 14 , and that the size of the matrix X representing the delay times is reduced from M ⁇ K to M ⁇ q.
  • the pseudo-inverse matrix X(hat) + represented by the above-mentioned equation (8) is calculated based on the delay times which have been determined to be shorter than the threshold value ⁇ th in the delay time grouping step ST 14 .
  • the size of the matrix X(hat)′ H X(hat)′ in the equation (8) on which the inverse matrix computation is performed is q ⁇ q, and that the size of the matrix is reduced by the delayed wave removal step ST 15 .
  • the processes of the arriving wave separation step ST 17 are performed.
  • the values a(hat) 1,1 , a(hat) 2,1 at the top are extracted from the respective column vectors y(hat)′ 1 , y(hat)′ 2 calculated in the manner described above, and output as the first and second direct wave components.
  • the arrival angle estimation step ST 18 the phase difference ⁇ between the first direct wave component a(hat) 1,1 and the second direct wave component a(hat) 2 , 1 extracted in the arriving wave separation step ST 17 are calculated, and the arriving direction of the direct wave is estimated based on the calculated phase difference.
  • the arrival angle estimation step ST 18 comprises a phase difference calculation step ST 80 , and an arrival angle calculation step ST 81 , as shown in FIG. 14 .
  • phase difference calculation step ST 80 the phase difference ⁇ between the direct wave component a(hat) 1,1 and the direct wave component a(hat) 2,1 is calculated.
  • the calculation is performed according to the above equation (14).
  • the arrival angle ⁇ is calculated from the phase difference ⁇ using the relation of the above equation (13).
  • the fifth embodiment is a receiving method corresponding to the second embodiment.
  • FIG. 15 shows a process procedure in the fifth embodiment of the present invention.
  • the receiving method shown in FIG. 15 is generally identical to the receiving method of FIG. 10 , but a threshold value determination step ST 31 is added.
  • the processes of the threshold value determination step ST 31 are similar to the processes performed by the threshold value determination unit 31 in FIG. 8 .
  • the processes of the threshold value determination step ST 31 are performed after the processes of the delay time estimation step ST 13 .
  • the threshold value ⁇ th is determined based on the delay times estimated in the delay time estimation step ST 13 .
  • the delay time grouping step ST 14 in FIG. 15 is generally identical to the delay time grouping step ST 14 in FIG. 10 , but differs in the following respects.
  • the predetermined threshold value ⁇ th is used, whereas in the delay time grouping step ST 14 in FIG. 15 , the threshold value ⁇ th determined in the threshold value determination step ST 31 is used.
  • the threshold value determination step ST 31 for example, an intermediate value between the minimum value and the maximum value of the delay times estimated in the delay time estimation step ST 13 is used as the threshold value ⁇ th .
  • a sum of the minimum value of the delay times estimated in the delay time estimation step ST 13 , and a predetermined value may be used as the threshold value ⁇ th .
  • a sum of the product of the difference between the maximum value and the minimum value of the delay times estimated in the delay time estimation step ST 13 , and a predetermined value larger than 0 and smaller than 1, and the above-mentioned minimum value may be used as the threshold value ⁇ th .
  • the threshold value ⁇ th may be any value as long as it is between the minimum value and the maximum value of the delay times estimated by the delay time estimation step ST 13 , and, the present embodiment is not limited to the manner of its calculation.
  • the delay times can be grouped into those which are shorter than the threshold value ⁇ th and those which are equal to or longer than the threshold value ⁇ th , and, therefore, part only of the arriving waves estimated in the transmission channel estimation step ST 12 can be removed.
  • the sixth embodiment is a receiving method corresponding to the third embodiment.
  • FIG. 16 shows a process procedure in the sixth embodiment of the present invention.
  • the receiving method shown in FIG. 16 is generally identical to the receiving method in FIG. 10 , but a delay time number discrimination step ST 32 is added.
  • the processes in the delay time number discrimination step ST 32 are similar to the processes performed by the delay time number discrimination unit 32 .
  • the delay time number discrimination step ST 32 is performed after the delay time estimation step ST 13 .
  • the delay time number discrimination step ST 32 a determination is made as to whether the number K of the delay times (corresponding to the number of the arriving waves) estimated in the delay time estimation step ST 13 is smaller than a predetermined threshold value K th .
  • the procedure proceeds to the step ST 14 . Subsequent processes are similar to those described in the first embodiment.
  • the procedure proceeds to the step ST 16 .
  • Such a column vector y(hat)′ n comprises the components corresponding to all the delay times ⁇ 1 to ⁇ K .
  • the number of the delay times corresponds to the number of the arriving waves.
  • the sixth embodiment has been described as a modification to the fourth embodiment. Similar modification can be applied to the fifth embodiment.
  • FIG. 1 , FIG. 8 , and FIG. 9 parts of the receiving apparatus according to the first, second and third embodiments, shown in FIG. 1 , FIG. 8 , and FIG. 9 (parts shown as functional blocks) may be implemented by a processing circuit.
  • the processing circuit may be dedicated hardware or a CPU executing programs stored in a memory.
  • FIG. 1 , FIG. 8 , and FIG. 9 may be implemented by separate processing circuits, or the functions of a plurality of parts may be implemented by a single processing circuit.
  • the processing circuit When the processing circuit is a CPU, the functions of the various parts of the receiving apparatus may be implemented by software, firmware, or a combination of software and firmware.
  • Software or firmware is described as programs, and stored in a memory.
  • the processing circuit implements the functions of the various parts by reading and executing the programs stored in the memory. That is, when the receiving apparatus is implemented by a processing circuit, it comprises a memory for storing programs which, when executed, cause the functions of the various parts shown in FIG. 1 , FIG. 8 , or FIG. 9 to be performed. These programs can be said to those causing a computer to execute the processes or their procedure in the receiving method implemented in the receiving apparatus.
  • part of the functions of the various parts of the receiving apparatus may be implemented by dedicated hardware and other part may be implemented by software or firmware.
  • processing circuit may realize the various functions described above by hardware, software, firmware or their combination.
  • FIG. 17 shows an example of a configuration in which the above-mentioned processing circuit is a CPU, and all the functions of the receiving apparatus are implemented by a computer (denoted by reference characters 100 ) comprising a single CPU, together with antenna elements 10 - 1 , 10 - 2 .
  • the computer 100 shown in FIG. 17 comprises a CPU 101 , a memory 102 , input units 103 - 1 , 103 - 2 , and an output unit 104 , which are interconnected by a bus 105 .
  • antenna elements 10 - 1 , 10 - 2 Connected to the input units 103 - 1 , 103 - 2 are antenna elements 10 - 1 , 10 - 2 .
  • Signals received by the antenna elements 10 - 1 , 10 - 2 are supplied to the CPU 101 via the input units 103 - 1 , 103 - 2 .
  • the CPU 101 operates according to the programs stored in the memory 102 , and performs the processes of the various parts of the receiving apparatus of the first, second or third embodiment, on the signals input via the input units 103 - 1 , 103 - 2 , and outputs the resultant output signals via the output unit 104 .
  • Effects similar to those described in connection with the receiving apparatus can also be obtained from the receiving method implemented in the receiving apparatus, programs for causing a computer to execute the processes performed by the various parts of the receiving apparatus or the processes in the receiving method, and a computer-readable recording medium in which the above-mentioned programs are stored.
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